How to simplify this fraction?

Can anyone show me how to simplify this fraction:

$$
\frac{(k + 1)((k + 1)+1)(2(k + 1)+1)}{6}\;\;.
$$

What can be factored out and so forth?

Thanks.

Answer

$$
\frac{(k+1)((k+1)+1)(2(k+1)+1)}{6}=\frac{(k+1)(k+2)(2k+3)}{6}
$$

Then if $k=2n$ you have

\begin{align*}
\frac{(k+1)(k+2)(2k+3)}{6}=&

\frac{(2n+1)(2n+2)(4n+3)}{6}\\
=&\frac{(2n+1)2(n+1)(4n+3)}{6}\\
=&\frac{(2n+1)(n+1)(4n+3)}{3}
\end{align*}

it's not so different if $k=2n+1$.
Then if you want you can consider in more detail: what if $n=2m$? And $n=2m+1$?
Enjoy!